The US also claimed in a background briefing that North Korean officials had failed to show up in Singapore to arrange logistics for the June meeting.

Mr Kim has indicated he wants a phased approach, with his steps met by reciprocal ones from the United States and the South - mainly on sanctions but also easing of the United States military presence in South Korea.

"I hope if the NK-US summit is successful, through the three-way summit, we can declare the end of the war", Moon said.

Former US ambassador to South Korea, Sung Kim, crossed into North Korea on Sunday to hold talks with Pyongyang's Vice-Foreign Minister, Choe Son Hui, a source familiar with the matter told the paper.

State department spokeswoman Heather Nauert said a "US delegation is in ongoing talks with North Korean officials" inside the demilitarised zone between North and South Korea that was created at the end of the Korean War.

Abe is considering visiting the United States for a summit with Trump before heading to Canada where leaders from the Group of Seven industrialized nations will gather on June 8 and 9, according to government sources. Pyongyang released three American hostages, agreed to the goals of peace on the Korean peninsula and complete denuclearization, and destroyed its only nuclear test site.

"I think the two leaders will sit down and they're going to have a great time, because really they have the same personality", he said on Sunday.

Libyan dictator Moammar Qaddafi agreed in 2003 to give up his weapons of mass destruction, including nuclear arms, in return for sanctions relief. When asked about the talks between Moon and Kim, the president replied, "the talks have gone very well". North Korea was the first to waver, threatening on May 15 that the fate of the meeting could be in jeopardy due to the U.S.'s military exercises with North Korea.

That revelation signals that Kim keenly wants the U.S. summit, and that Moon is happy to play the role of an intermediary between Pyongyang and Washington.

Kim, in a telling line from a dispatch issued by the North's state-run news service earlier Sunday, "expressed his fixed will on the historic (North Korea)-US summit talks".

He told reporters Friday that "everybody plays games", and said: "They very much want to do it, we want to do it, we'll see what happens".

Trump rattled the region on Thursday by cancelling his meeting with Kim, citing "open hostility" from Pyongyang.

The North has previously used the term to demand the United States pull out its 28,500 troops in South Korea and withdraw its so-called "nuclear umbrella" security commitment to South Korea and Japan.

Sen. Marco Rubio, Florida Republican, said he's skeptical that Mr. Kim will agree to completely give up his country's nuclear capabilities, saying the leader has an nearly emotional attachment to them and that they make him feel prestigious and powerful.

Moon, who returned to Seoul on Thursday morning after meeting Trump in Washington earlier this week in a bid to keep the summit on track as initially planned, for June 12 in Singapore, was due to announce details of the meeting with Kim early on Sunday. He added that he expected the practical talks and summit to go "very smoothly".